How do you simplify # i^37#?

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Answer 1 · 2018-04-27T22:28:29

#i#

First, recall that

#i=sqrt(-1)#

#i^2=-1#

#i^3=-1*sqrt(-1)=-i#

#i^4=-1*-1=1#

Whenever the exponent on #i# is a multiple of #4#, it will evaluate to #1#, as imaginary numbers follow a pattern.

#36# is a multiple of #4#, so we know #i^36=1#. We can rewrite #i^37# as

#i^36*i#

#=1*i=color(blue)(i)#

Thus, #i^37=i#

Hope this helps!